The CH equation is integrable in several different senses, such as: It is bi-Hamiltonian and possesses a Lax pair [1]}, [2]}, its solutions provides metrics for a two-dimensional Riemannian manifold with constant and negative Gaussian curvature [3]}, [4]}, [5]}, [6]} (pseudo-spherical equations) and is geometrically integrable as well [3]}. For further details on integrable or pseudo-spherical equations, see [8]} or [9]}, [10]}, respectively.
